Introduction to Digital Logic Assignment

1. Give the general expression for a positional number in base r of (n+1) Integer digits and m fractional digits. (Recall weights of an (n+1) digit integer are numbered from n to zero.)

2. Convert the following hexadecimal numbers to octal using binary as the intermediary:

a. (17F.2A59)₁₆ :

b. (2B.36EF)₁₆ :

c. (DEAF.ED)₁₆ :

2. Convert the following octal numbers to hexadecimal using binary as the intermediary:

a. (476.225)₈ :

b. (5123.357)₈ :

c. (5655.6655)₈ :

3. Express the following in one's complement format using 8 bits:

a. (?27)₈ :

b. ?(1)₁₀ :

c. ?(1011.101)₂ :

d. (6 7/8)₁₀ :

e. (?010.1010)₂ :

4. Express the following in nine's complement format using 8 digits:

a. (?884.631)₁₀ :

b. ?(3407.28)₁₀ :

c. ?(120.485)₁₀ :

d. (?61.8267)₁₀ :

e. (?5976.08)₁₀ :

5. Express the following in two's complement format using 8 bits:

a. ?(1)₁₀ :

b. (?5.3)₁₆ :

c. (?111.001)₂ :

d. (?1011.110)₂ :

e. (5A)₁₆ :

6. Express the following in sign-magnitude format using 8 bits or 8 digits as appropriate:

a. (?2701.43)₁₀ :

b. (?FC4B.6)₁₆ :

c. (?11 100.1)₂ :

d. (4423.012)₅ :

e. (0.654 32)₈ :

7. Express the following as 6 digit decimal numbers in binary coded decimal (BCD) format:

a. (380.27)₁₀ :

b. (?92.55)₁₀ :

c. (?867.09)₁₀ :

8. Express the following as 6 digit decimal numbers in excess three (XS-3) format:

a. (?1.3872)₁₀ :

b. (?901.56)₁₀ :

c. (987.12)₁₀ :

9. Convert from the indicated base to decimal. Truncate fractional numbers to 4 digits:

a. (5314.24)₆ :

b. (3412.03)₅ :

c. (3B7C.14)₁₃ :

10. Convert from decimal to the indicated base. Truncate fractional numbers to 4 digits:

a. (2989.71)₁₀ to base 16:

b. (5423.15)₁₀ to base 6:

c. (238.36)₁₀ to base 11: